Monomiality principle, Sheffer-type polynomials and the normal ordering problem
نویسندگان
چکیده
منابع مشابه
Monomiality principle, Sheffer-type polynomials and the normal ordering problem
We solve the boson normal ordering problem for ( q(a†)a+ v(a†) )n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] = 1. This consequently provides the solution for the exponential e †)a+v(a†)) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle...
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We construct explicit representations of the Heisenberg-Weyl algebra [P, M ] = 1 in terms of ladder operators acting in the space of Sheffer-type polynomials. Thus we establish a link between the monomiality principle and the umbral calculus. We use certain operator identities which allow one to evaluate explicitly special boson matrix elements between the coherent states. This yields a general...
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We solve the boson normal ordering problem for (q(a)a + v(a)) with arbitrary functions q and v and integer n, where a and a are boson annihilation and creation operators, satisfying [a, a] = 1. This leads to exponential operators generalizing the shift operator and we show that their action can be expressed in terms of substitutions. Our solution is naturally related through the coherent state ...
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A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials of binomial and Sheffer types. The connecti...
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2006
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/30/1/012